Backward
shift operators provide a general class of linear dynamical systems on
infinite dimensional spaces. Despite linearity, chaos is a phenomenon that
occurs within this context. In this paper we give characterizations for
chaos in the sense of
Auslander and Yorke [1980] and in the sense of Devaney
[1989] of weighted backward shift operators and perturbations of the identity
by backward shifts on a wide class of sequence spaces. We cover and unify
a rich variety of known examples in different branches of applied mathematics.
Moreover, we give new examples of chaotic backward shift operators. In
particular we prove that the
differential operator $I+D$ is Auslander-Yorke chaotic
on the most usual spaces of analytic functions.